Genetic association studies aim to map disease genes through comparisons of frequencies of genetic variants among affected and unaffected individuals. Due to usually weak associations between genetic variants and disease, it is critical to apply powerful statistical tests to maximize the chance to locate disease loci. We propose developing novel and powerful multi-locus methods based on penalized regression to detect genetic association for population- or family-based studies with un- phased genotype data. Specifically, statistical methods and theory will be developed and evaluated for statistical inference and prediction based on penalized regression with novel nonconvex penalties for linear models, generalized linear models and generalized estimating equations. We will apply the developed methods to large cohorts in the Candidate gene Association Resource (CARe) for multi- locus analysis to discover atrial fibrillation (AF)-associated variants, possibly by considering gene by gene and gene by environment interactions. Known and newly discovered genetic and other risk factors will be used to predict AF.